Ultrafine micropipettes, with tip diameters of 0.1 micron and smaller, are required for penetration of extremely small animal cells for injection, electrophysiological study and the like. Such micropipettes may be formed by subjecting a heated length of glass tubing to an extremely light tensile load, usually less than one pound. According to one method this light tension is maintained until the glass tubing is extended in length by a predetermined amount. Then, after the heating element is cooled, the tubing was then subjected to a hard pull of up to 100 pounds to complete the ultrafine tip. This method is described in a commentary written by K. T. Brown and D. G. Flaming, the present inventor, and published in the Volume 2, 1977 issue of Neuroscience published by Pergamon Press (Great Britain). That method has worked satisfactorily for most purposes in producing the desired tip diameter. However, the extent of elongation of the glass tubing during the light pull, does not govern the ultimate taper and length of the micropipette tip achieved after the hard pull. While it is desirable to have only a slight taper at the tip in order to minimize animal cell distortion as penetration is advanced, there may be excessive electrical resistance in a tip that is too long. Moreover, the extreme flexibility of a long, thin tip may render it unsuitable for reaching target cells that are deeply buried.